The observed Standard Model (SM) quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa (CKM) mixing pattern are described in an SU(8) theory through its realistic symmetry breaking pattern with three intermediate stages, which rely on a set of d = 5 gravity-induced operators that break the emergent global symmetries in the chiral fermion sector, as well as the precise identifications of all non-trivially embedded SM flavors.

China

Ning Chen

Ying-nan Mao

Zhaolong Teng

The Standard Model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an SU(8) theory

The 1973 Kobayashi–Maskawa paper proposed a compelling link between Cabibbo’s flavor mixing scheme and <inline-formula><tex-math id='TM0001' notation='LaTeX'>${\mathcal {C}}$</tex-math></inline-formula> <inline-formula><tex-math id='TM0002' notation='LaTeX'>${\mathcal {P}}$</tex-math></inline-formula> violation but, since it required the existence of six quarks at a time when the physics community was happy with only three, it received zero attention. However, two years after the paper appeared&#8212;at which time it had received a grand total of two citations&#8212;the charmed quark was discovered and it finally got some notice and acceptance. After this stumbling start, it subsequently emerged as the focal point of an enormous amount of experimental and theoretical research activity. In an invited talk at a KEK symposium to celebrate the 50th anniversary of the KM paper, I reviewed some of the less well known circumstances that occurred in the years preceding and following the paper&#8217;s appearance. Some spoilers: (i)&#160;Kobayashi and Maskawa (and a number of other Japanese physicists) were convinced about the existence of the charmed quark nearly three years before its &#8220;discovery&#8221; at Brookhaven and SLAC. (ii)&#160;The matrix provided in their seminal 1973 paper was mathematically incorrect. Another version that was in common use for the following 12 years was technically correct, but not really a rotation matrix. (iii)&#160;The CKM matrix <inline-formula><tex-math id='TM0003' notation='LaTeX'>${\mathcal {C}}$</tex-math></inline-formula> <inline-formula><tex-math id='TM0004' notation='LaTeX'>${\mathcal {P}}$</tex-math></inline-formula>&#160;phase was only measurable because of the very specific hierarchy of the flavor mixing angles and meson masses. (iv)&#160;Similarly, the neutrino mixing discovery, and the PMNS matrix measurability were only possible because of favorable values of the neutrino mass differences and mixing angles. In addition I include some speculations about what may be in store for the future.

South Korea

Stephen Lars Olsen

The Curious Early History of the Cabibbo–Kobayashi–Maskawa Matrix: Miracles Happen!

The LHCb experiment has been in operation since 2009 and has provided measurements of the Kobayashi–Maskawa matrix with unprecedented precision. 50 years after the original paper we are in the position to pin down the parameters of the theory, or possibly to show its limitations. In these proceedings the status of LHCb is shown from a historical perspective, along with some anecdotes.

Netherlands

Patrick Koppenburg

Flavor physics at LHCb: 50 years of the Kobayashi–Maskawa paradigm

The Kobayashi–Maskawa (KM) hypothesis about the existence of a third generation of quarks represents a cornerstone of the Standard Model (SM). Fifty years after this seminal paper [M. Kobayashi and T. Maskawa, Prog. Theor. Phys. <bold>49</bold>, 652 (1973)], flavor physics continues to represent a privileged observatory on physics occurring at high energy scales. In this paper I first review this statement using general effective-theory arguments, highlighting some interesting modern lessons from the KM paper. I then discuss some novel extensions of the SM based on the concept of flavor deconstruction: the hypothesis that gauge interactions are manifestly flavor-non-universal in the ultraviolet. The phenomenological consequences of this class of models are also briefly illustrated.

Switzerland

Gino Isidori

Flavor physics beyond the Standard Model and the Kobayashi–Maskawa legacy

Dark pion is a promising candidate for the strongly interacting massive particle dark matter. A large pion self-coupling m  π /f  π  tends to be required for correct relic abundance, and hence the partial-wave amplitudes can violate the perturbative unitarity even for the coupling within naïve perturbative regime. We improve the partial-wave amplitudes in order to satisfy the optical theorem. We demonstrate that the improvement is relevant only for semi-relativistic pions, and thus this does not affect the self-scattering cross section at the cosmic structures. We also discuss the impact of the improvement of the πππ → ππ scattering process, and we find that there is an upper bound on m  π  at which the correct relic abundance is never achieved even at large m  π /f  π  due to the optical theorem.

Poland

Japan

Ayuki Kamada

Shin Kobayashi

Takumi Kuwahara

Perturbative unitarity of strongly interacting massive particle models

We discuss cosmological constraints on a dark scalar particle mixing with the Standard Model Higgs boson. We pay particular attention to the dark scalar production process when the reheating temperature of the Universe is very low, which allows us to give a conservative limit on the low-mass scalar particle. We also study the effect of the self-interaction of the dark scalars and find this has a significant impact on the cosmological constraints. We obtain the most conservative cosmological constraint on the dark scalar, which is complementary to accelerator experiments and astrophysical observations.

Masahiro Ibe

Yuhei Nakayama

Satoshi Shirai

Cosmological constraints on dark scalar

The Fermi constant <math><mrow><msub><mrow><mi>G</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> is extremely well measured through the muon lifetime, defining one of the key fundamental parameters in the standard model (SM). Therefore, to search for physics beyond the SM (BSM) via <math><msub><mi>G</mi><mi>F</mi></msub></math>, the constraining power is determined by the precision of the second-best independent determination of <math><msub><mi>G</mi><mi>F</mi></msub></math>. The best alternative extractions of <math><msub><mi>G</mi><mi>F</mi></msub></math> proceed either via the global electroweak (EW) fit or from superallowed <math><mi>β</mi></math> decays in combination with the Cabibbo angle measured in kaon, <math><mi>τ</mi></math>, or <math><mi>D</mi></math> decays. Both variants display some tension with <math><msub><mi>G</mi><mi>F</mi></msub></math> from muon decay, albeit in opposite directions, reflecting the known tensions within the EW fit and hints for the apparent violation of Cabibbo-Kobayashi-Maskawa unitarity, respectively. We investigate how BSM physics could bring the three determinations of <math><msub><mi>G</mi><mi>F</mi></msub></math> into agreement using SM effective field theory and comment on future perspectives.

CERN

Andreas Crivellin

Martin Hoferichter

Claudio Andrea Manzari

Fermi Constant from Muon Decay Versus Electroweak Fits and Cabibbo-Kobayashi-Maskawa Unitarity

The asymmetric dark matter (ADM) scenario solves the baryon-dark matter coincidence problem when the dark matter (DM) mass is of   <math> <mi>O</mi> <mfenced> <mn>1</mn> </mfenced> </math>  $$ \mathcal{O}(1) $$  GeV. Composite ADM models based on QCD-like strong dynamics are particularly motivated since the strong dynamics naturally provides the DM mass of   <math> <mi>O</mi> <mfenced> <mn>1</mn> </mfenced> </math>  $$ \mathcal{O}(1) $$  GeV and the large annihilation cross-section simultaneously. In those models, the sub-GeV dark photon often plays an essential role in transferring the excessive entropy in the dark sector into the visible sector, i.e., the Standard Model sector. This paper constructs a chiral composite ADM model where the U(1) D  gauge symmetry is embedded into the chiral flavor symmetry. Due to the dynamical breaking of the chiral flavor symmetry, the model naturally provides the masses of the dark photon and the dark pions in the sub-GeV range, both of which play crucial roles for a successful ADM model.

Keiichi Watanabe

Chiral composite asymmetric dark matter

We discuss gauge mediated supersymmetry breaking models which explain the observed muon anomalous magnetic moment and the Higgs boson mass simultaneously. The successful explanation requires the messenger sector which violates the relation motivated by the grand unification theory (GUT). The naive violation of the GUT relation, however, ends up with the CP problem. We propose a model in which the phases of the gaugino masses are aligned despite the violation of the GUT relation. We also consider a model which generates the μ-term and the additional Higgs soft masses squared without causing CP violation. As a result, we find a successful model which explains the muon anomalous magnetic moment and the Higgs boson mass. The model is also free from the CP, flavor-changing neutral current and the lepton flavor violation problems caused by the subdominant gravity mediation effects. The lightest supersymmetric particles are gravitino/goldstini and the next-to-lightest ones are the Wino/Higgsinos in the typical parameter space. We also study the LHC constraints.

Muon g − 2 in gauge mediation without SUSY CP problem

Recently, the chiral superconductivity of the cosmic string in the axion model has gathered attention. The superconductive nature can alter the standard understanding of the cosmology of the axion model. For example, a string loop with a sizable super-conducting current can become a stable configuration, which is called a Vorton. The superconductive nature can also affect the cosmological evolution of the string network. In this paper, we study the stability of the superconducting current in the string. We find the superconductivity is indeed stable for a straight string or infinitely small string core size, even if the carrier particles are unstable in the vacuum. However we also find that the carrier particle decays in a curved string in typical axion models, if the carrier particles are unstable in the vacuum. Accordingly, the lifetime of the Vorton is not far from that of the carrier particle in the vacuum.